We create a list of prime numbers, primes. We reverse the list, primes_rev. We create new lists from applying math operations to each element of both lists, sum, mul, sub, div.
Then we plot the new lists.

Interesting pictures, nice to look at and search for meaning. Nowadays, computer experimentation is being used a fair bit to generate plausible conjectures. In this case, you will see if you try that similar plots can be obtained from using most sequences which do not grow too fast. You might for instance repeat with $a_n=n/\log(n)$. The striking picture for mul is basically the general shape of $y=x(N-x)$. The picture for sum is interesting.
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André NicolasAug 4 '11 at 2:38

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I agree with André. The overall trends are just what you'd expect from any sequence of numbers that grows slightly faster than linearly. For example, here's your second plot for if the $n$th entry were $n \log n$; try replacing the multiplication with the other operators and see that you get essentially the same shape as your graphs.
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RahulAug 4 '11 at 2:47